## An Introduction to Formal LogicFormal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic. |

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Some explanations are drawn out, but this drawn out approach gives Smith the opportunity to repeat himself - thus making the material easier to retain. It may take me longer than other works to cover a subject, but I feel like my ability to recall the material is far better than other Formal Logic book's i've attempted to read. Also, unlike most Formal Logic texts, solutions to the many exercises are provided online.

### Contents

What is logic? | 1 |

Validity and soundness | 9 |

Patterns of inference | 18 |

The counterexample technique | 29 |

Proofs | 36 |

Validity and arguments | 44 |

Logic formal and informal | 51 |

Three prepositional connectives | 53 |

After prepositional logic | 192 |

Quantifiers | 194 |

QL introduced | 202 |

QL explored | 210 |

More QL translations | 219 |

Introducing QL trees | 228 |

The syntax of QL | 242 |

Qvaluations | 250 |

The syntax of PL | 63 |

The semantics of PL | 72 |

As and Bs Ps and Qs | 82 |

Truth functions | 88 |

Tautologies | 101 |

Tautological entailment | 107 |

Propositional logic | 123 |

PLC and the material conditional | 125 |

More on the material conditional | 137 |

Introducing PL trees | 145 |

Rules for PL trees | 157 |

PLC trees | 171 |

PL trees vindicated | 179 |

Trees and proofs | 185 |

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### Common terms and phrases

3xFx Angharad apply assigns atomic wffs basic brackets chapter claim Clark Kent closed tree complex wffs conclusion false conjunction consider constant construction tree contradiction deductively valid disjunction domain of discourse English equivalent evaluate example existential existential quantifier expressions extension F F F F T F F T T F function Hence Here's inference step inferential instantiate invalid involving Jack Leibniz's Law logicians loves Jill material conditional means negation open path P A Q pair philosopher PL wffs Plato possible predicate premisses and conclusion premisses true proof propositional logic propositions q-valid q-valuation q-value QL trees quantifiers restricted quantifications saturated set schematic variables semantic sentences Socrates someone Superman Suppose tautologically entail tautologically valid Theory of Descriptions things tion translation true premisses truth truth-functional truth-table test truth-value universal quantification universally quantified unpack variables Vx(Fx D Gx Vx(Gx VxFx Vy(Fy